The solution of the system of equations is
x = -13/20 , y = 9/2 , z = 19/20
Given, a system of equations
x + 5y - 3z = 19
2x - 3y + 4z = -11
4x + y - 2z = 0
On multiplying eq (1) by 2, we get
2x + 10y - 6z = 38
On subtracting eq (1) and (2), we get
13y - 10z = 49 ... (4)
Now, On multiplying eq (2) by 2, we get
4x - 6y + 8z = -22
On subtracting eq (3) and (2), we get
7y - 10z = 22 ... (5)
Now, on subtracting eq (4) and (5), we get
6y = 27
y = 9/2
On substituting the value of y in Eq (5), we get
z = 19/20
Now, On substituting the value of y & z in Eq (1), we get
x + 5(9/2) - 3(19/20) = 19
x + 45/2 - 57/20 = 19
x + 393/20 = 19
x = -13/20
Hence, the solution of the system of equations is
x = -13/20 , y = 9/2 , z = 19/20
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a study investigated whether there are differences between the mean iq level of people who were raised by their biological parents and those who were raised by someone else.what is the null hypothesis in this case?
There is no difference between the mean IQ levels of people who were reared by their natural parents and those who were not.
Hypothesis.1) Graphically, the shaded area before the downturn, represents the set of values for Rents greater than $700. So, rent (y) > 7002) Graphically, the shaded area after the downturn, represents the set of values for Rents lesser than $700. So, rent 700 <y<0A hypothesis is an educated prediction regarding the solution to a scientific question that is supported by sound reasoning. It is the expected result of the experiment, however it is not proof in an experiment.Depending on the information received, it might be supported or might not be supported at all.learn more about hypothesis click here:
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30/100 + 5/10
please help me.
Answer:
4/5
Step-by-step explanation:
hope it helped :)
prove that every non-empty finite set has the same number of subsets of even size as it has subsets of odd size.
It is proved that every non-empty finite set has the same number of subsets of even size as it has subsets of odd size
The set's members are numbered 1, 2, 3, 4,..., n.
There is a set with an odd number of items that corresponds to every subset with an even number of elements in the following manner:
Delete 1 from the set to create one with an odd number of elements if it is a member of the set with an even number of elements.
Add 1 to the set to create a set with an odd number of items if it isn't already a member of the set with an even number of elements.
Let's say the set has the numbers 1, 2, 3, and 4. The relationship between sets with even numbers of elements and sets with odd numbers of elements is as follows:
even odd
∅ ↔ {1}
{1,2}↔ {2}
{1,3}↔ {3}
{1,4}↔ {4}
{2,3}↔{1,2,3}
{2,4}↔{1,2,4}
{3,4}↔{1,3,4}
{1,2,3,4↔{1,2,3,4}
Therefore, it is demonstrated that any non-empty finite set has the same number of even-sized and odd-sized subsets.
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If the federal reserve decreases the reserve rate from 5% to 4%, how does this affect the money supply from a $50,000 deposit after fractional-reserve banking has multiplied it?.
If reserve rate decreases from 5% to 4% then money supply of $50000
deposits increases .i.e bank can save $2000 and can lend $48000.
The reserve ratio is the percentage of reserves (or cash deposits) that a bank must keep and not lend out. The higher the reserve requirement, the less money a bank can potentially lend—but this extra cash also prevents a bank from failing and strengthens its balance sheet. Still, when the reserve ratio rises, monetary policy is considered contractionary, and when it falls, monetary policy is considered expansionary.
Given this, the reserve rate falls from 5% to 4%.
$50000 is the initial deposit.
If the reserve ratio is 5%, the bank must keep 50000*0.05 = $2500 in reserve and may make loans totaling 50000-2500=$47500.
If the reserve ratio is reduced to 4%, a bank with $50000 in deposits must save 50000*0.04 = $2000 before it can lend $48000.
Thus, if reserve ratio decreases then the money supply increases.
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9. Prove that y = (x - 2)2 - 9 and y = (x + 1)(x - 5) represent the same parabola
On simplifying the given equations y = (x - 2)² - 9 and y = (x + 1)(x - 5), they represent the same parabola which is y = x² - 4x - 5
What is equation of parabola?
The equation of a parabola can be expressed in standard form and vertex form. The standard form of a parabola is y = ax² + bx + c where a, b, and c are constants, and a does not equal 0.
The vertex form of a parabola is y = a(x - h)² + k. The coordinates (h,k) represent the vertex of the parabola.
We can check if the given equations represent the same parabola by simplifying them to standard form of equation of parabola.
According to the given equation:
y = (x - 2)² - 9
y = x² - 4x + 4 - 9
∴ y = x² - 4x - 5 ------ 1)
Similarly simplifying other equation
y = (x + 1)(x - 5)
y = x² - 5x + x - 5
y = x² - 4x - 5 ----- 2)
Clearly equation 1) and 2) represent the same parabola having equation
y = x² - 4x - 5
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Tom needs to buy plastic forks. Brand A has a box of 36 forks for $1.54. Brand B has a box of 48 forks for $1.66. Find the unit price for each brand. Then state which brand is the better buy based on the unit price. Round your answers to the nearest cent. pls answer
Brand B will be the best because it costs less each fork.
Brand B has price of $0.03 per forks .
What is unit price ?The cost per unit of an item is represented by the unit price. To get the unit price of an item, we divide the price of a specific number of units by the number of units.It is computed by multiplying the total number of units produced by the sum of fixed and variable costs.Here given,
Given that Brand A charges $1,54 for a package of 36forks,
Then the price per fork will be:
= $1.54 / 36
= $0.042
Given that Brand B charges $1.66 for a box of 48 forks,
Then the price per fork will be:
= $1.66 / 48
= $ 0.034
Since brand B has lower cost per fork ,
Brand B will therefore be the finest brand with $0.03 per forks price.
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Read the description of a proportional relationship. Ever since Brian was a small child, his favorite food has always been carrots. He likes them so much he wants to plant a garden in his backyard just to grow carrots. There is a proportional relationship between the size of Brian's garden (in square feet), x, and the number of carrots he can grow at a time, y. The equation that models this relationship is y=4x. What size garden does Brian need to grow 20 carrots at a time?
The size of the garden That Brian need to grow 20 carrots at a time is 5 square feet
The size of the Brian's garden in square feet = x
The number of carrots that he can grow at a time = y
The equation that models the relationship is
y = 4x
The means the number of carrots that he can grow at a time is directly proportional to the size of the Brian's garden,
The number of carrots that he need to grow = 20 carrots
Substitute the values in the equation and find the value of x
20 = 4x
The size of the garden x = 20/4
= 5 square feet
Hence, the size of the garden That Brian need to grow 20 carrots at a time is 5 square feet
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The amount owed is $10865, based on the given parameters
How to determine the amount owed in six years?The given parameters about the compound interest are
Principal Amount, P = $5300
Interest Rate, R = 8%
Time, t = 6 years
To calculate the amount owed, we make use of the following formula
A = P + CI
Where
Compound interest, CI = P(1 + R)^t - P
So, the equation becomes
A = P + P(1 + R)^t - P
Evaluate the like terms
A = P(1 + R)^t
In this question, the formula is given as
A = P(1 + r/n)^nt
Where
n = 12, i.e compounded monthly
Substitute the known values in the above equation
A = 5300 * (1 + 8%/12)^(6*12)
Express 8% as decimal
A = 5300 * (1 + 0.08/12)^(6*12)
Evaluate the sum
A = 5300 * (1.01)^(6*12)
Evaluate the exponent
A = 5300 * 2.05
Evaluate the product
A = 10865
Hence, the value of the amount after 6 years is $10865
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25 rules in 5 groups
There are five rules in one group
From the question, we have
25 rules in 5 groups
In one group = 25/5 = 5 rules
There are five rules in one group
Divide:
Repetitive subtraction is the process of division. It is the multiplication operation's opposite. It is described as the process of creating equitable groups. When dividing numbers, we divide a larger number down into smaller ones such that the larger number obtained will be equal to the multiplication of the smaller numbers. One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things. It is a mathematical operation used for equal distribution and equal grouping.
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Given the parent function y=x. Find the equation of a second line that has a negative y intercept and a positive slope.
For the parent function y = x, the equation of the line has a negative y-intercept and a positive slope will be y = mx + c where c < 0 and m > 0.
What is the slope-intercept form of a line?
When you know the slope of the line to be examined and the point given is also the y-intercept, you can use the slope-intercept formula y = mx + b. (0, b). The y value of the y-intercept point is represented by b in the formula.
For the given parent function y = x.
Comparing with the slope-intercept form y = mx + c, we get
slope(m) = 1, and the y-intercept is c = 0;
So we can make one line such that it has a negative y-intercept and a positive slope.
y = mx + c, where c < 0 and m > 0.
Hence, for the parent function y = x, the equation of the line has a negative y-intercept and a positive slope will be y = mx + c where c < 0 and m > 0.
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The diameter of a circle is 52.6 millimeters. What is the circle's area? Use 3.14 for and round your answer to the nearest hundredth.
the circle's area is approximately 2173.22 mm².We can find the radius of the circle by dividing the diameter by 2
what is diameter ?
Diameter is a straight line passing through the center of a circle or sphere and connecting two points on the circumference. It is the longest chord of the circle.
In the given question,
The diameter of a circle is 52.6 millimeters.
We can find the radius of the circle by dividing the diameter by 2:
radius = diameter/2 = 52.6/2 = 26.3 mm
Now, we can use the formula for the area of a circle:
area = π × radius²
Plugging in the values we have:
area = 3.14 × 26.3² = 3.14 × 691.69 ≈ 2173.21 mm²
Rounding to the nearest hundredth, we get:
area ≈ 2173.21 ≈ 2173.22 mm²
Therefore, the circle's area is approximately 2173.22 mm².
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for the following distribution. x p(x) 0 0.027 1 0.189 2 0.441 3 0.343 what is the variance of the distribution?
Variance of the given distribution is equal to 0.63.
As given in the question,
Given data for the distribution is equal to :
X: 0 1 2 3
P(x): 0.027 0.189 0.441 0.343
Variance for the given distribution is equal to
= E(x²) - {E(x)}²
Now , Value of E(x) can be calculated using the formula,
E(x) = [tex]\sum x_{i} P( x_{i} )[/tex]
= (0)(0.027) + (1)(0.189) + (2)(0.441) + (3)(0.343)
= 0.189 + 0.882 + 1.029
= 2.1
E(x²) = [tex]\sum x_{i} ^{2} P(x_{i})[/tex]
= (0)²(0.027) + (1)²(0.189) + (2)²(0.441) + (3)²(0.343)
= 0.189 + 1.764 + 3.087
= 5.04
Variance = E(x²) - {E(x)}²
= 5.04 - (2.1)²
= 5.04 - 4.41
= 0.63
Therefore, variance of the given distribution is equal to 0.63.
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What is the solution to n/4 = -12.4?
Answer:
Step-by-step explanation:
-12.4 x 4 = -49.6
n = -49.6
Answer:
n = -49.6
Step-by-step explanation:
1. Multiply both sides of the equation by 4
[tex](4)\frac{n}{4}=(4)-12.4[/tex]2. Simplify the expression
n=(4)-12.4n= -4 * 12.4n=-49.6Mia owns a small business selling bagels. She knows that in the last week 85 customers paid cash, 5 customers used a debit card, and 16 customers used a credit card. Based on these results, express the probability that the next customer will pay with cash as a percent to the nearest whole number.
The probability that the next consumer will use cash as payment is 85/106
85 customers made cash payments.
5 customers used debit cards in total.
16 customers used credit cards in total.
The probability that the following consumer will make a cash payment must be calculated as a fraction in its simplest form.
Total clients: 85 + 5 + 16 = 106
There were 85 successful outcomes (Customers who paid cash)
Therefore, the probability will be: =85/106 = 0.801
Therefore, the probability that the following customer will pay with cash is 85/106.
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Answer:
≈ 80%
Step-by-step explanation:
Based on these results, express the probability that the next customer will pay with cash as a percent to the nearest whole number.
85 cash, 5 debit card, and 16 credit card.
85+5+16= 106
There were a toal of 106 customers. 85 paid with cash.
Probability the next customer will pay with cash:
85/106= 0.801886...
0.801886... ×100% ≈ 80.1887%
≈ 80%
what is the correct setup to finding the slope of a line that passes through the points (6,-3),(-2,7)
Answer:
slope = - [tex]\frac{5}{4}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (6, - 3 ) and (x₂, y₂ ) = (- 2, 7 )
m = [tex]\frac{7-(-3)}{-2-6}[/tex] = [tex]\frac{7+3}{-8}[/tex] = [tex]\frac{10}{-8}[/tex] = - [tex]\frac{5}{4}[/tex]
The slope of a line that passes through the points (6,-3),(-2,7) is -5/4.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,
then the equation of line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)
To find the slope of a line that passes through the points (6,-3),(-2,7):
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
m = (7+3)/(-2-6)
m = -10/8
m = -5/4
Therefore, the slope is -5/4.
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Solve the equation.
(x+3)^2-5=0
And
Solve the equation.
(2x+1)(x-5)=0
The solution to equation (x+3)² - 5 = 0 is x = -3 +√5 and x = -3 - √5. The solution to equation (2x+1)(x-5)=0 is x = -1/2 and x = 5.
What is a quadratic function?The quadratic function is defined as a function containing the highest power of a variable is two.
To determine the solution to equation (x+3)² - 5 = 0
(x+3)² - 5 = 0
x² + 9 + 6x - 5= 0
x²+ 6x + 4 = 0
Using the quadratic formula to solve the above quadratic function
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\dfrac{-6\pm \sqrt{6^2-4\cdot \:1\cdot \:4}}{2\cdot \:1}[/tex]
[tex]\sqrt{6^2-4\cdot \:1\cdot \:4}[/tex] = 2√5
x = -6± 2√5 / 2
x = -3± √5
x = -3 +√5 and x = -3 - √5
To determine the solution to equation (2x+1)(x-5)=0
(2x+1)(x-5)=0
(2x+1) = 0 and (x-5)=0
2x = -1 and x = 5
x = -1/2 and x = 5
Thus, the solution to equation (x+3)² - 5 = 0 is x = -3 +√5 and x = -3 - √5. The solution to equation (2x+1)(x-5)=0 is x = -1/2 and x = 5.
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what are all the fractions that fit between 1/2 and 1
There are infinitely more possibilities, but the midpoint between 1/2 and 1 is 3/4.
what is fraction?
An element of a whole or, more broadly, any number of equal pieces, is represented by a fraction. When used in conversational English, a fraction indicates the number of components of a particular size, as in one-half, eight-fifths, and three-quarters.
For any two numbers a and b, the average 1/2(a + b) is lies between them.
Here, the given two numbers are 1/2 and 1.
So, to find the fraction between 1/2 and 1 we can form the average:
1/2(1/2 + 1) = 1/2(3/2) = 3/4
Hence, the fraction that fit between 1/2 and 1 is 3/4.
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Consider a bank with two tellers. Three people, Alice, Betty, and Carol enter the bank at almost the same time and in that order. Alice and Betty go directly into service while Carol waits for the first available teller. Suppose that the service times for each customer are exponentially distributed with mean of 4 minutes. Betty finishes and leaves the bank. Carol goes to the available teller. What's the probability Alice leaves before carol?
The probability that Alice leaves before Carol is 0.5 according to the given information.
What is meant by probability?Probability is a branch of mathematics that deals with numerical descriptions of how likely an event or statement is to occur.
If X1 and X2 are both exponential distributions with parameters 1 and 2, respectively, then
P(X₁< X₂)= λ₁/(λ₁+λ₂ )
And P(X>s+t/x>s)=P(X>t), if X≈exp(μ)
Here, Let [tex]X_{A}[/tex], [tex]X_{C}[/tex] denote the service times for Alice and Carol
And also given that,
E[ [tex]X_{A}[/tex]]=1/μ
E[ [tex]X_{A}[/tex]]=4
E[ [tex]X_{C}[/tex]]=4
E[ [tex]X_{A}[/tex]]=E[ [tex]X_{C}[/tex]]=4
So, [tex]X_{A}[/tex], [tex]X_{C}[/tex] ≈exp(1/4)
Now, when Betty completes his service, Alice is still being served, and the remaining time required to complete his service is exp(1/4).
Because the exponential distribution has no memory.
So, P( [tex]X_{A}[/tex]< [tex]X_{C}[/tex] )= λ₁/ λ₁+ λ₂
=(1/4)/((1/4)+(1/4))
=(1/4)/(1/2)
=0.5
As a result, the probability that Alice leaves before Carol is 0.5.
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How does electron pair repulsion determine the molecular shape/molecule geometry?.
Yes, the electron pair repulsion determines the molecular shape, we can use VSEPR to find out how.
What is VSEPR theory?
The amount of valence electron pairs present in the outermost shell is used by the valence shell electron repulsion theory (VSEPR) to predict the structure of molecules.
The number of valence shell electron bond pairs between atoms in a molecule is used in the valence shell electron repulsion theory (VSEPR), a model for predicting 3D molecular form.
VSEPR theory predicts that BeF2 should be a linear molecule, with a 180o angle between the two Be-F bonds.
The VSEPR theory, therefore, predicts a trigonal planar geometry for the BF3 molecule, with an F-B-F bond angle of 120o.
we can predict that a tetrahedral molecule in which the H-C-H bond angle is 109o28'.
Hence we can predict the molecular shape, using VSEPR theory.
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Write an equation representing the y-intercept (0,4), (4,2)
Answer:
y = -1/2x + 4
Step-by-step explanation:
Use the slope formula (change in y divided by change in x) to find the slope. (-1/2). Then pick one of the points and plug it back into the new equation using -1/2 as your slope.
In Game 1, Emerson struck out 30 times in 90 times at bat. In Game 2, he struck out 40 times in 120 times at bat. In Game 3, Emerson struck out 42 times in 140 times at bat. What is the percent of times her hit the ball.
The percent of times that Emerson hit the ball, given the number of times that he struck out was 68 %
How to find the percent of times?First, find the total number of times that Emerson had at bat:
= Game 1 + Game 2 + Games 3
= 90 + 120 + 140
= 350 times
The number of times Emerson missed was:
= 30 + 40 + 42
= 112 times
The number of times the ball was hit is therefore:
= 350 - 112
= 238 times
The percent of time the ball was hit:
= 238 / 350
= 68 %
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sample Response: The sample is from the right population, his customers. However, because he is surveying such a small number of people and only asking his best customers (who are probably the most satisfied, or they would not buy so much from him), the results are going to be biased, most likely positive, and not representative of his entire customer base.
What did you include in your response? Check all that apply.
The sample size is too small.
Only sending the survey to his best customers will yield biased results, most likely in the positive direction.
The sample is not representative of the entire population.
The thing to include in the response regarding the sampling include:
The sample size is too small.Only sending the survey to his best customers will yield biased results, most likely in the positive direction.The sample is not representative of the entire population.What is sampling?Sampling is the process of selecting the group from which you will collect data for your research. For example, if you want to know what students think at your university, you could survey 100 of them. In statistics, sampling allows you to test a hypothesis about a population's characteristics.
The act of deciding how many observations or replicates to include in a statistical sample is known as sample size determination. The sample size is an important aspect of any empirical study.
In this case, the sample size wasn't a true reflection of the customers.
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Please Help ASAP! I NEED THIS NOW!.
The quadratic equation is [tex]x^2+x-12[/tex]
What is quadratic equation?
Quadratics can be defined as a polynomial equation of a second degree, which implies that it comprises a minimum of one term that is squared. It is also called quadratic equations. The general form of the quadratic equation is:
ax² + bx + c = 0
where x is an unknown variable and a, b, c are numerical coefficients.
Given, the roots of quadratic equation as (3,-4).
The formula to find the quadratic equation, as
x2 – (Sum of the roots)x + Product of the roots = 0
Sum of roots = 3-4
=-1
Product of roots = 3(-4) = -12
The quadratic equation is
x²+x-12
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In triangle ABC, angler A is 35 degrees, and angle b is 20 degrees. Select all triangles which are similar to triangle ABC
The triangle which are similar to ABC are:
Triangle DEF where ∠D is 35° and ∠E is 20°.Triangle JKL where ∠J is 35° and ∠L is 125°.Triangle MNO where ∠N is 20° and ∠O is 125°.The connecting of three non-collinear points results in a triangle, which is a three-sided closed-plane object. Triangles can be classified into three categories based on their side properties: equilateral, scalene, and isosceles.
We know that the when we sum all the interior angles of a triangle, we get 180°.
Given that, A triangle ABC has ∠A = 35° and ∠B = 20°.
∴ ∠C = 180° - 35° - 20°.
∠C = 125°.
Triangle will be similar if every corresponding angle of different triangles has the same measure. So, Triangles that are similar to triangle ABC is triangle DEF where ∠D is 35° and ∠E is 20° and triangle JKL where ∠J is 35° and ∠L is 125° and triangle MNO where ∠N is 20° and ∠O is 125°.
Therefore, triangle DEF, JKL and MNO are similar to triangle ABC.
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The given question is incomplete. Here is the complete Question:
The local orchestra has been invited to play at a festival. There are 111 members of the orchestra and 6 are licensed to drive large multi-passenger vehicles. Busses hold 25 people but are much more expensive to rent. Passenger vans hold 12 people. Create a system of equations to find the smallest number of busses the orchestra can rent.
The system of equations to find the smallest number of buses the orchestra can rent will be b + v ≤ 6 and 25b + 12v ≥ 111.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
Given that, Six of the orchestra's 111 musicians hold driving licenses for big, multi-passenger vehicles. 25 people can fit on a bus, but renting one is far more expensive. 12 persons can fit in a passenger van.
The system of equations to find the smallest number of busses the orchestra can rent is,
The total number of buses :
b + v ≤ 6
The total number of passengers.
25b + 12v ≥ 111 - - - - (2)
Thus, the system of equations to find the smallest number of buses the orchestra can rent will be b + v ≤ 6 and 25b + 12v ≥ 111.
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Help help help help help
theorem of sines answer: A
6-(2x+4) is less than or equal to 10
Step-by-step explanation:
6-(2x+4) is less than or equal to 10
6-(2x+4) ≤ 10
6 - 2x - 4 ≤ 10
combine like terms on left side:
2 - 2x ≤ 10
subtract 2 from both sides:
2 - 2x - 2 ≤ 10 - 2
- 2x ≤ 8
divide both sides by -2: (remember, when dividing by a negative number you must FLIP the sign direction)
- 2x/-2 ≥ 8/-2
x ≥ 8/-2
x ≥ -4
[-4, ∞)
Step-by-step explanation:
6-(2x+4) is less than or equal to 10
6-(2x+4) ≤ 10
6 - 2x - 4 ≤ 10
combine like terms on left side:
2 - 2x ≤ 10
subtract 2 from both sides:
2 - 2x - 2 ≤ 10 - 2
- 2x ≤ 8
divide both sides by -2: (remember, when dividing by a negative number you must FLIP the sign direction)
- 2x/-2 ≥ 8/-2
x ≥ 8/-2
x ≥ -4
[-4, ∞)
Jocelyn and her children went into a movie theater and she bought $75.50 worth of candies and pretzels. Each candy costs $4.75 and each pretzel costs $3.50. She bought a total of 18 candies and pretzels altogether. Determine the number of candies and the number of pretzels that Jocelyn bought.
The number of candies bought = 10
The number of pretzels bought = 8
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
Let,
x = number of candies bought
y = number of pretzels bought.
The equations that describe the given problem are:
4.75 x + 3.5 y = 75.50..........(1)
x + y = 18
x = 18 - y.................(2)
Substitute equation 2 in equation 1,
4.75 (18 - y) + 3.5 y = 75.50
85.5-4.75y+3.5y=75.50
85.5-1.25y=75.50
1.25y=85.5-75.50=10
y=8
Substitute y=8 into x = 18 - y.
x=18-8=10
The number of candies bought is 10, and the number of pretzels bought is 8.
To learn more about the equation from the given link
https://brainly.com/question/28218072
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a) Use the diagram to work out the solution to these simultaneous equations: b) Substitute your x value into each of the equations and solve to find y. What do you notice about i) the value of y in each equation? ii) the value of y compared to the solution in part a)? Y 10 9 8 7 6 5 4 3 32 y = 2x + 1 y = -x + 7 1 1 2 3 4 y=2x+1 5 y=-x +7 6 7 8 9 10
Answer:
(a) (x, y) = (2, 5)
(bi) y = 5, y = 5; the values are the same
(bii) the values are the same as in part (a)
Step-by-step explanation:
You want the solution and some observations about it for the system of equations ...
y = 2x +1y = -x +7a) Solution
The graph shows the lines cross at the point (x, y) = (2, 5).
The solution to the equations is (x, y) = (2, 5).
b) Values of yi) For x=2, the value of y in the first equation is ...
y = 2(2) +1 = 4 +1 = 5
For x=2, the value of y in the second equation is ...
y = -(2) +7 = -2 +7 = 5
ii) The values of y are the same, and match the value we found in part (a).
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Additional comment
The purpose of the exercise is to get you to see that the value of x that is the solution makes both equations have the same value of y, and that is the value of y that is the solution.
The graph is a plot of the y-value for each x-value. Where the lines cross, the y-values are the same for that x-value. That point of intersection of the lines is the solution to the system of equations: the values of x and y satisfy both equations at that point.
An angle measures 37.6 degrees less than the measure of its complementary angle. What is the measure of each angle
Answer:
x = 27.1 y = 62.9 x + y = 90
Explaination:
Let's say you have 2 complimentary angles, x and y
So x + y = 90
if x is 35.8 degrees less than the measure of a complementary angle, then x = y - 35.8
Putting this into our x + y = 90 equation, we get (y - 35.8) + y = 90
2y - 35.8 = 90
2y = 90 + 35.8
2y = 125.8
y = 125.8/2 = 62.9 degrees.
so x = 62.9 - 35.8 = 27.1 degrees.
